SYDNEY (Reuters) - Support for Australian Prime Minister Malcolm Turnbull is at its lowest level since his election last year, according to an opinion poll on Tuesday, fuelling speculation of more political upheaval in a country that has seen four leaders in six years.

The Australian newspaper poll showed Turnbull's net satisfaction rating, which measures the difference between those who are satisfied and those who are dissatisfied, had fallen to 29 points, some 11 points lower than after his July 2 election.

Turnbull enjoys only marginal more support from the electorate than Australia's previous prime minister, Tony Abbott, whom he toppled in a party room coup year ago due to poor voter support.

When asked about the poll, Turnbull said he was unconcerned about the findings.

"The important thing for me, as prime minister, and for my government, is to get on with the job of governing and delivering, and that is what we're doing," Turnbull told reporters in Brisbane.

Turnbull, who's progressive reputation is seen at odds with the powerful conservative wing of his own Liberal Party, has been mired by recent internal divisions.

He and Abbott, now a backbencher, become embroiled in a public row over Australia's strict gun laws last week, while a spat between two of the country's senior legal officers further fueled tensions.

Australia's Solicitor-General Justin Gleeson, who is tasked with giving the government legal advice, on Monday resigned after accusing Senator George Brandis, the country's most senior legal officer, of failing to consult him around changes to terror laws and a proposed national vote for same-sex marriage.

While Turnbull has sought to redirect focus towards delivering his agenda of "jobs and growth", his legislative agenda faces an uncertain future with the government holding only a slim majority in the parliament.

"Without changing course in policy, Turnbull's poll numbers will continue to go south and given he used them as justification to oust a sitting prime minister, he is going to find himself under pressure," said Haydon Manning, professor of political science, Finders University.